I don't think there's anything on the coding and billing side that you can do about this since you can only code from what you have - this is the type of thing that you're just going to have to fight out with the payer.
My recommendation would be to start with an appeal with a letter of explanation giving the facts that you have and the reason why the second screening was reasonable and done according to standards of medical care. You may be able to request records from the original physician's procedure to support this.
If that doesn't work then these charges, in my opinion, should become patient responsibility since the denial is due to the service not being a covered benefit. Patients are ultimately responsible for knowing what their benefits are under their plans, and if they receive non-covered services, they should expected to be responsible for it. If they do not agree, then it would really be up to them to contest this with their own insurance company.
It's possible the payer might say that this is not medically necessary and that the patient cannot be billed, but I would contest that since screenings are preventive, not diagnostic or therapeutic, procedures so the concept of medical necessity should not apply.
Lastly, if this is a recurring problem, you may want to educate your providers to identify this situation when taking the patients' histories, before the procedure takes place. This way, an authorization or verification of benefits might be obtained in advance, or the patient can be cautioned that the service might not be covered and then can make a decision as to whether or not they wish to assume responsibility for it in the event of a denial.
Not sure if that helps any?